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   <h4 class="subsectionHead"><span class="titlemark">2.8   </span> <a 
 id="x13-420002.8"></a>3d Continuum Elements</h4>
<!--l. 1083--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.1   </span> <a 
 id="x13-430002.8.1"></a>LSpace element</h5>
<!--l. 1085--><p class="noindent" >Implementation of Linear 3d eight - node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4300233">33<!--tex4ht:ref: lspacesummary --></a>. <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4300112"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure11.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;12: </span><span  
class="content">LSpace element (Node numbers in black, side numbers in blue, and surface numbers in red).</span></div><!--tex4ht:label?: x13-4300112 -->
                                                                                           
                                                                                           
<!--l. 1094--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1096--><p class="noindent" >
<div class="table">
<!--l. 1096--><p class="noindent" ><a 
 id="x13-4300233"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-34" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-34-1g"><col 
id="TBL-34-1"></colgroup><colgroup id="TBL-34-2g"><col 
id="TBL-34-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-34-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-34-1-2"  
class="td11"><!--l. 1096--><p class="noindent" ><span 
class="cmbx-10">lspace</span>                                                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-2-2"  
class="td11"><!--l. 1096--><p class="noindent" >Linear isoparametric brick element                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-34-3-2"  
class="td11"><!--l. 1096--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-34-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-4-2"  
class="td11"><!--l. 1097--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to set the number of integration points (possible
completions are 1, 8 (default), or 27).                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-5-2"  
class="td11"><!--l. 1098--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-6-2"  
class="td11"><!--l. 1099--><p class="noindent" >Linear approximation of displacement and geometry.        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-7-2"  
class="td11"><!--l. 1100--><p class="noindent" >Full integration of all strain components.                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-8-2"  
class="td11"><!--l. 1101--><p class="noindent" >Adaptivity support, Geometric nonlinearity support.        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-9-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-9-2"  
class="td11"><!--l. 1102--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-10-2"  
class="td11"><!--l. 1103--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-34-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-11-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-34-11-2"  
class="td11"><!--l. 1104--><p class="noindent" >0,1,2.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-34-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-34-12-2"  
class="td11"><!--l. 1105--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-34-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-34-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-34-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;33: </span><span  
class="content">lspace element summary</span></div><!--tex4ht:label?: x13-4300233 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.2   </span> <a 
 id="x13-440002.8.2"></a>LSpaceBB element</h5>
<!--l. 1110--><p class="noindent" >Implementation of 3d brick eight - node linear approximation element with selective integration of deviatoric and
volumetric strain contributions (B-bar formulation) for incompressible problems. Features and description identical to
conventional lspace element, see section &#x00A0;<a 
href="#x13-430002.8.1">2.8.1<!--tex4ht:ref: lspacesect --></a>.
<!--l. 1115--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.3   </span> <a 
 id="x13-450002.8.3"></a>QSpace element</h5>
<!--l. 1116--><p class="noindent" >Implementation of quadratic 3d 20-node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4500234">34<!--tex4ht:ref: qspacesummary --></a>. <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4500113"></a>
                                                                                           
                                                                                           
<!--l. 1121--><p class="noindent" >
<img 
src="elementlibmanual-figure12.png" alt="PIC"  
> <img 
src="elementlibmanual-figure13.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;13: </span><span  
class="content">QSpace element.</span></div><!--tex4ht:label?: x13-4500113 -->
                                                                                           
                                                                                           
<!--l. 1125--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1127--><p class="noindent" >
<div class="table">
<!--l. 1127--><p class="noindent" ><a 
 id="x13-4500234"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-35" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-35-1g"><col 
id="TBL-35-1"></colgroup><colgroup id="TBL-35-2g"><col 
id="TBL-35-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-35-1-2"  
class="td11"><!--l. 1127--><p class="noindent" ><span 
class="cmbx-10">qspace</span>                                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-2-2"  
class="td11"><!--l. 1127--><p class="noindent" >Quadratic isoparametric brick element                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-35-3-2"  
class="td11"><!--l. 1127--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-4-2"  
class="td11"><!--l. 1128--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to set the number of integration points (possible
completions are 1, 8 (default), or 27).                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-5-2"  
class="td11"><!--l. 1129--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-6-2"  
class="td11"><!--l. 1130--><p class="noindent" >Quadratic approximation of displacement and geometry.   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-7-2"  
class="td11"><!--l. 1131--><p class="noindent" >Full integration of all strain components.                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-8-2"  
class="td11"><!--l. 1132--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-9-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-35-9-2"  
class="td11"><!--l. 1133--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-10-2"  
class="td11"><!--l. 1134--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-11-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-35-11-2"  
class="td11"><!--l. 1135--><p class="noindent" >0,1,2.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-35-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-35-12-2"  
class="td11"><!--l. 1136--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-35-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-35-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;34: </span><span  
class="content">qspace element summary</span></div><!--tex4ht:label?: x13-4500234 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.4   </span> <a 
 id="x13-460002.8.4"></a>LTRSpace element</h5>
<!--l. 1141--><p class="noindent" >Implementation of tetrahedra four-node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4600235">35<!--tex4ht:ref: LTRSpacesummary --></a>. Following node numbering convention is adopted (see also Fig.&#x00A0;<a 
href="#x13-4600114">14<!--tex4ht:ref: lintetrahedron_fig --></a>):
     <ul class="itemize1">
     <li class="itemize">Select a face that will contain the first three corners. The excluded corner will be the last one.
     </li>
     <li class="itemize">Number these three corners in a counterclockwise sense when looking at the face from the excluded
     corner.</li></ul>
<!--l. 1150--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4600114"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure14.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;14: </span><span  
class="content">LTRSpace element. Definition and node numbering convention.</span></div><!--tex4ht:label?: x13-4600114 -->
                                                                                           
                                                                                           
<!--l. 1157--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1159--><p class="noindent" >
<div class="table">
<!--l. 1159--><p class="noindent" ><a 
 id="x13-4600235"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-36" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-36-1g"><col 
id="TBL-36-1"></colgroup><colgroup id="TBL-36-2g"><col 
id="TBL-36-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-36-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-36-1-2"  
class="td11"><!--l. 1159--><p class="noindent" ><span 
class="cmbx-10">LTRSpace</span>                                                     </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-2-2"  
class="td11"><!--l. 1159--><p class="noindent" >Linear tetrahedra element                                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-36-3-2"  
class="td11"><!--l. 1159--><p class="noindent" >-                                                                            </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-36-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-4-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-4-2"  
class="td11"><!--l. 1161--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-5-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-5-2"  
class="td11"><!--l. 1162--><p class="noindent" >Linear approximation of displacements and geometry using
linear volume coordinates.                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-6-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-6-2"  
class="td11"><!--l. 1163--><p class="noindent" >Full integration of all strain components using four point
Gauss integration formula.                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-7-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-7-2"  
class="td11"><!--l. 1164--><p class="noindent" >Adaptivity support, Geometric nonlinearity support.        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-8-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-8-2"  
class="td11"><!--l. 1165--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-9-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-9-2"  
class="td11"><!--l. 1166--><p class="noindent" >Surface and Edge loadings supported.                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-10-1"  
class="td11">Nlgeo                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-10-2"  
class="td11"><!--l. 1167--><p class="noindent" >0,1,2.                                                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-36-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-36-11-2"  
class="td11"><!--l. 1168--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-36-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-36-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-36-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;35: </span><span  
class="content">LTRSpace element summary</span></div><!--tex4ht:label?: x13-4600235 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.5   </span> <a 
 id="x13-470002.8.5"></a>QTRSpace element</h5>
<!--l. 1173--><p class="noindent" >Implementation of tetrahedra ten-node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4700236">36<!--tex4ht:ref: QTRSpacesummary --></a>. Following node numbering convention is adopted (see also Fig.&#x00A0;<a 
href="#x13-4700115">15<!--tex4ht:ref: qtetrahedron_fig --></a>):
<!--l. 1177--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4700115"></a>
                                                                                           
                                                                                           
<!--l. 1180--><p class="noindent" >
<img 
src="elementlibmanual-figure15.png" alt="PIC"  
> <img 
src="elementlibmanual-figure16.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;15: </span><span  
class="content">QTRSpace element. Definition and node numbering convention.</span></div><!--tex4ht:label?: x13-4700115 -->
                                                                                           
                                                                                           
<!--l. 1185--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1187--><p class="noindent" >
<div class="table">
<!--l. 1187--><p class="noindent" ><a 
 id="x13-4700236"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-37" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-37-1g"><col 
id="TBL-37-1"></colgroup><colgroup id="TBL-37-2g"><col 
id="TBL-37-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-37-1-2"  
class="td11"><!--l. 1187--><p class="noindent" ><span 
class="cmbx-10">QTRSpace</span>                                                     </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-2-2"  
class="td11"><!--l. 1187--><p class="noindent" >3D tetrahedra element with quadratic interpolation         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-37-3-2"  
class="td11"><!--l. 1187--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-4-2"  
class="td11"><!--l. 1188--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to alter the default integration formula (possible
completions are 1, 4 (default), 5, 11, 15, 24, and 45 point
intergartion formulas).                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-5-2"  
class="td11"><!--l. 1189--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-6-2"  
class="td11"><!--l. 1190--><p class="noindent" >Quadratic approximation of displacements and geometry
using linear volume coordinates.                                   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-7-2"  
class="td11"><!--l. 1191--><p class="noindent" >Full integration of all strain components using four point
Gauss integration formula.                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-8-2"  
class="td11"><!--l. 1192--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-9-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-37-9-2"  
class="td11"><!--l. 1193--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-10-2"  
class="td11"><!--l. 1194--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-11-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-37-11-2"  
class="td11"><!--l. 1195--><p class="noindent" >0,1,2.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-37-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-37-12-2"  
class="td11"><!--l. 1196--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-37-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-37-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;36: </span><span  
class="content">QTRSpace element summary</span></div><!--tex4ht:label?: x13-4700236 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.6   </span> <a 
 id="x13-480002.8.6"></a>LWedge element</h5>
<!--l. 1201--><p class="noindent" >Implementation of wedge six-node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4800237">37<!--tex4ht:ref: LWedgesummary --></a>. Following node numbering convention is adopted (see also Fig.&#x00A0;<a 
href="#x13-4800116">16<!--tex4ht:ref: linwedge_fig --></a>):
<!--l. 1205--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4800116"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure17.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;16: </span><span  
class="content">LWedge element. Node numbering convention in black, edge numbering in blue and face numbering
in red.</span></div><!--tex4ht:label?: x13-4800116 -->
                                                                                           
                                                                                           
<!--l. 1212--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1214--><p class="noindent" >
<div class="table">
<!--l. 1214--><p class="noindent" ><a 
 id="x13-4800237"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-38" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-38-1g"><col 
id="TBL-38-1"></colgroup><colgroup id="TBL-38-2g"><col 
id="TBL-38-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-38-1-2"  
class="td11"><!--l. 1214--><p class="noindent" ><span 
class="cmbx-10">LWedge</span>                                                         </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-2-2"  
class="td11"><!--l. 1214--><p class="noindent" >3D wedge six-node finite element with linear interpolation</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-38-3-2"  
class="td11"><!--l. 1214--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-4-2"  
class="td11"><!--l. 1215--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to alter the default integration formula (possible
completions  are  2  (default)  and  9  point  integration
formulas).                                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-5-2"  
class="td11"><!--l. 1216--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-6-2"  
class="td11"><!--l. 1217--><p class="noindent" >Linear approximation of displacements and geometry.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-7-2"  
class="td11"><!--l. 1218--><p class="noindent" >Full integration of all strain components using four point
Gauss integration formula.                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-8-2"  
class="td11"><!--l. 1219--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-9-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-38-9-2"  
class="td11"><!--l. 1220--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-10-2"  
class="td11"><!--l. 1221--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-11-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-38-11-2"  
class="td11"><!--l. 1222--><p class="noindent" >0,1,2.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-38-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-38-12-2"  
class="td11"><!--l. 1223--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-38-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-38-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;37: </span><span  
class="content">LWedge element summary</span></div><!--tex4ht:label?: x13-4800237 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">2.8.7   </span> <a 
 id="x13-490002.8.7"></a>QWedge element</h5>
<!--l. 1227--><p class="noindent" >Implementation of wedge fifteen-node finite element. Each node has 3 degrees of freedom. The element features are
summarized in Table&#x00A0;<a 
href="#x13-4900238">38<!--tex4ht:ref: QWedgesummary --></a>. Following node numbering convention is adopted (see also Fig.&#x00A0;<a 
href="#x13-4900117">17<!--tex4ht:ref: qwedge_fig --></a>):
<!--l. 1231--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x13-4900117"></a>
                                                                                           
                                                                                           
<!--l. 1234--><p class="noindent" >
<img 
src="elementlibmanual-figure18.png" alt="PIC"  
> <img 
src="elementlibmanual-figure19.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;17: </span><span  
class="content">QWedge element. Node numbering convention in black, edge numbering in blue and face numbering
in red.</span></div><!--tex4ht:label?: x13-4900117 -->
                                                                                           
                                                                                           
<!--l. 1239--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1241--><p class="noindent" >
<div class="table">
<!--l. 1241--><p class="noindent" ><a 
 id="x13-4900238"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-39" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-39-1g"><col 
id="TBL-39-1"></colgroup><colgroup id="TBL-39-2g"><col 
id="TBL-39-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-39-1-2"  
class="td11"><!--l. 1241--><p class="noindent" ><span 
class="cmbx-10">QWedge</span>                                                        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-2-2"  
class="td11"><!--l. 1241--><p class="noindent" >3D   wedge   six-node   finite   element   with   quadratic
interpolation                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-39-3-2"  
class="td11"><!--l. 1241--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-4-2"  
class="td11"><!--l. 1242--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to alter the default integration formula (possible
completions  are  2  (default)  and  9  point  integration
formulas).                                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-5-2"  
class="td11"><!--l. 1243--><p class="noindent" >Three
dofs (u-displacement, v-displacement, w-displacement) are
required in each node.                                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-6-2"  
class="td11"><!--l. 1244--><p class="noindent" >Quadratic approximation of displacements and geometry.  </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-7-2"  
class="td11"><!--l. 1245--><p class="noindent" >Full integration of all strain components using four point
Gauss integration formula.                                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-8-2"  
class="td11"><!--l. 1246--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-9-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-39-9-2"  
class="td11"><!--l. 1247--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-10-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-10-2"  
class="td11"><!--l. 1248--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-11-1"  
class="td11">Nlgeo </td> <td  style="white-space:wrap; text-align:left;" id="TBL-39-11-2"  
class="td11"><!--l. 1249--><p class="noindent" >0,1,2.</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-39-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-12-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-39-12-2"  
class="td11"><!--l. 1250--><p class="noindent" >Reliable                                                                  </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-13-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-39-14-"><td  style="white-space:nowrap; text-align:left;" id="TBL-39-14-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;38: </span><span  
class="content">QWedge element summary</span></div><!--tex4ht:label?: x13-4900238 -->
</div><hr class="endfloat" />
</div>
</div>
                                                                                           
                                                                                           
                                                                                           
                                                                                           
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